Why the blender browser plugin is not updated?
As an alternative.  You can also have a look at blend4web which can directly export to an HTML file and since it uses WebGL, no browser plugin is needed.   It can also export to a more programmer oriented format for use with some of their other tools.

So far as I know, it is not yet capable of using BGE logic bricks however b4w is being updated regularly and can already be used to make really nice looking browser games.  There is also a lot of documentation available so getting started should not be too difficult.

https://www.blend4web.com/en/

Here is a BA.org thread that is currently being maintained by an employee of blend4web  http://blenderartists.org/forum/showthread.php?333214-Blend4Web-a-3D-web-framework-for-Blender-artists